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Jan 22 Significant Figures

In science, significant figures mean all of the numbers, besides the leading and cushioning zeroes. (e.g. 12,000,000,000,000,000,000,000 only has 2 significant digits, but it has 21 zeroes. There are a lot of other specific rules.

Zeroes between a number count, like 4009 has four significant digits.

Zeroes placed after digits AFTER a decimal point count. (7.90 has three significant digits), because the extra zero expresses the accuracy with which the number should be expressed.

Zeroes placed before digits AFTER a decimal point DON'T count (0.0000350 has 3 significant digits)

1000 has one significant digit, but 1000.0 has five significant digits, and 1000. has 4 digits.

Some general rules:

All non-zero digits count.

All zeroes between those digits count.

ROUNDING

Rounding is really confusing when using significant figures. It's completely normal, but if it gets confusing at .5

At n.5 it goes to the closest even number. So, at 11.5, it rounds to 12, and at 12.5 it rounds to 12. This is done to avoid bias when rounding, it goes up half the time, and it goes down half the time.

OPERATIONS

For operations with significant figures it is essential to round only on the FINAL ANSWER. Otherwise, it'd become pretty inaccurate.

So, for 143/0.02010, you notice that 143 only has three significant figures, and .02010 has four (the last zero is important). So, it becomes 7114.4278607, but it should only have three significant figures, and since the 4 in the ones place rounds down, it becomes 7110.

So the rules are:

For addition/subtraction, you take the one with the fewest decimal places, and use the same number of decimal for your final answer. For multiplication/division, the final answer has the same number of significant figures as the number with the fewest significant figures.